{"paper":{"title":"Family of explicitly diagonalizable weighted Hankel matrices generalizing the Hilbert matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Pavel Stovicek, Tomas Kalvoda","submitted_at":"2015-06-02T21:14:57Z","abstract_excerpt":"A three-parameter family $B=B(a,b,c)$ of weighted Hankel matrices is introduced with the entries \\[ B_{j,k}=\\frac{\\Gamma(j+k+a)}{\\Gamma(j+k+b+c)}\\,\\sqrt{\\frac{\\Gamma(j+b)\\Gamma(j+c)\\Gamma(k+b)\\Gamma(k+c)}{\\Gamma(j+a)\\, j!\\,\\Gamma(k+a)\\, k!}}\\,, \\] $j,k\\in\\mathbb{Z}_{+}$, supposing $a$, $b$, $c$ are positive and $a<b+c$, $b<a+c$, $c\\leq a+b$. The famous Hilbert matrix is included as a particular case. The direct sum $B(a,b,c)\\oplus B(a+1,b+1,c)$ is shown to commute with a discrete analog of the dilatation operator. It follows that there exists a three-parameter family of real symmetric Jacobi m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01064","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}